`BookProof.ChapterScaledDotProduct.rademacherMean_dot_sq_of_unit_entries` {k : Fin d → ℝ} (hk : ∀ i, (k i) ^ 2 = 1) : rademacherMean (fun x => (dot (signVec x) k) ^ 2) = (d : ℝ)

Proved

BookProof.ChapterScaledDotProduct.rademacherMean_dot_sq_of_unit_entries

by leonardopedro · Oct 9, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterScaledDotProduct.

BookProof.ChapterScaledDotProduct.rademacherMean_dot_sq_of_unit_entries {k : Fin d → ℝ} (hk : ∀ i, (k i) ^ 2 = 1) : rademacherMean (fun x => (dot (signVec x) k) ^ 2) = (d : ℝ)

Formalization note: Lean 4 identifier BookProof.ChapterScaledDotProduct.rademacherMean_dot_sq_of_unit_entries.

Preamble

-- Generated from ChapterScaledDotProduct.lean — theorem BookProof.ChapterScaledDotProduct.rademacherMean_dot_sq_of_unit_entries
import Definitions.Def_ChapterSoftmaxSharpness
import Mathlib
import Definitions.Def_ChapterScaledDotProduct
open BookProof.ChapterScaledDotProduct


open scoped BigOperators

noncomputable section


open BookProof.ChapterSoftmaxSharpness

variable {d : ℕ}

Formal statement

theorem BookProof.ChapterScaledDotProduct.rademacherMean_dot_sq_of_unit_entries {k : Fin d → ℝ} (hk : ∀ i, (k i) ^ 2 = 1) :
    rademacherMean (fun x => (dot (signVec x) k) ^ 2) = (d : ℝ) := by sorry

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